On the containment problem for fat points ideals and Harbourne’s conjecture

2020 ◽  
Vol 148 (6) ◽  
pp. 2411-2419 ◽  
Author(s):  
Ştefan O. Tohǎneanu ◽  
Yu Xie
Keyword(s):  
Fat Points ◽  
Containment Problem

scholarly journals On Segre's bound for fat points inPn

2016 ◽  
Vol 220 (6) ◽  
pp. 2307-2323 ◽  
Author(s):  
Edoardo Ballico ◽  
Olivia Dumitrescu ◽  
Elisa Postinghel
Keyword(s):  
Fat Points

Separators of fat points in Pn

2010 ◽  
Vol 324 (7) ◽  
pp. 1492-1512 ◽  
Author(s):  
Elena Guardo ◽  
Lucia Marino ◽  
Adam Van Tuyl
Keyword(s):  
Fat Points

The Containment Problem

2020 ◽  
pp. 77-80
Author(s):  
Enrico Carlini ◽  
Huy Tài Hà ◽  
Brian Harbourne ◽  
Adam Van Tuyl
Keyword(s):  
Containment Problem

The Containment Problem: Background

2020 ◽  
pp. 71-75
Author(s):  
Enrico Carlini ◽  
Huy Tài Hà ◽  
Brian Harbourne ◽  
Adam Van Tuyl
Keyword(s):  
Containment Problem

scholarly journals Compression of Phylogenetic Networks and Algorithm for the Tree Containment Problem

2019 ◽  
Vol 26 (3) ◽  
pp. 285-294 ◽  
Author(s):  
Andreas D.M. Gunawan ◽  
Hongwei Yan ◽  
Louxin Zhang
Keyword(s):  
Phylogenetic Networks ◽  
Containment Problem

Fat Points in ℙ1× ℙ1and Their Hilbert Functions

2004 ◽  
Vol 56 (4) ◽  
pp. 716-741 ◽  
Author(s):  
Elena Guardo ◽  
Adam Van Tuyl
Keyword(s):  
Finite Number ◽  
Hilbert Function ◽  
Free Resolution ◽  
Hilbert Functions ◽  
Minimal Free Resolution ◽  
Fat Points ◽  
Fat Point ◽  
Point Scheme

AbstractWe study the Hilbert functions of fat points in ℙ1× ℙ1. IfZ⊆ ℙ1× ℙ1is an arbitrary fat point scheme, then it can be shown that for everyiandjthe values of the Hilbert functionHZ(l,j) andHZ(i,l) eventually become constant forl≫ 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ℙ1× ℙ1. This enables us to compute all but a finite number values ofHZwithout using the coordinates of points. We also characterize the ACM fat point schemes using our description of the eventual behaviour. In fact, in the case thatZ⊆ ℙ1× ℙ1is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.

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